
theorem
  9817 is prime
proof
  now
    9817 = 2*4908 + 1; hence not 2 divides 9817 by NAT_4:9;
    9817 = 3*3272 + 1; hence not 3 divides 9817 by NAT_4:9;
    9817 = 5*1963 + 2; hence not 5 divides 9817 by NAT_4:9;
    9817 = 7*1402 + 3; hence not 7 divides 9817 by NAT_4:9;
    9817 = 11*892 + 5; hence not 11 divides 9817 by NAT_4:9;
    9817 = 13*755 + 2; hence not 13 divides 9817 by NAT_4:9;
    9817 = 17*577 + 8; hence not 17 divides 9817 by NAT_4:9;
    9817 = 19*516 + 13; hence not 19 divides 9817 by NAT_4:9;
    9817 = 23*426 + 19; hence not 23 divides 9817 by NAT_4:9;
    9817 = 29*338 + 15; hence not 29 divides 9817 by NAT_4:9;
    9817 = 31*316 + 21; hence not 31 divides 9817 by NAT_4:9;
    9817 = 37*265 + 12; hence not 37 divides 9817 by NAT_4:9;
    9817 = 41*239 + 18; hence not 41 divides 9817 by NAT_4:9;
    9817 = 43*228 + 13; hence not 43 divides 9817 by NAT_4:9;
    9817 = 47*208 + 41; hence not 47 divides 9817 by NAT_4:9;
    9817 = 53*185 + 12; hence not 53 divides 9817 by NAT_4:9;
    9817 = 59*166 + 23; hence not 59 divides 9817 by NAT_4:9;
    9817 = 61*160 + 57; hence not 61 divides 9817 by NAT_4:9;
    9817 = 67*146 + 35; hence not 67 divides 9817 by NAT_4:9;
    9817 = 71*138 + 19; hence not 71 divides 9817 by NAT_4:9;
    9817 = 73*134 + 35; hence not 73 divides 9817 by NAT_4:9;
    9817 = 79*124 + 21; hence not 79 divides 9817 by NAT_4:9;
    9817 = 83*118 + 23; hence not 83 divides 9817 by NAT_4:9;
    9817 = 89*110 + 27; hence not 89 divides 9817 by NAT_4:9;
    9817 = 97*101 + 20; hence not 97 divides 9817 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9817 & n is prime
  holds not n divides 9817 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
